Garlic is a national treasure in many cuisines. This soup comes from Spain, where it's often accentuated with sweet, smoky peppers (pimenton de la Vera) and spicy chorizo sausage. The soup is excellent without any additions, but feel free to improvise!
Place the butter and oil in a large, heavy stockpot and warm over low heat. Add the onions and garlic; cook, stirring frequently, until the onions are golden brown and the garlic is tender, 35 to 45 minutes. Watch carefully to make sure the onions and garlic don't burn.
Wrap the parsley, thyme, peppercorns, and bay leaf in a square of cheesecloth and tie with string to make a bouquet garni. Place the packet in the stockpot, then add the chicken stock and bread cubes. Raise the heat to high and bring the soup to the start of a boil. Then lower the heat to maintain a gentle simmer. Cook until the bread softens to the point of disintegration, about 15 minutes.
Remove the bouquet garni and discard. Add the half and half and purée the soup in a food processor or with an immersion blender until smooth. Season to taste with salt and pepper, and serve hot.